Transcription

1 Projectile motion with "measure Dynamics" TEP Related topics Parabolic trajectory, uniformly accelerated motion, and ballistics Principle A steel sphere is launched by a ballistic unit and the resulting trajectory is filmed with the aid of a video camera. The "measure Dynamics" software is used to demonstrate the dependence of the trajectory on the launching angle ϕ and on the initial velocity, and to determine the range and height of the trajectory. In addition, the resulting trajectory is integrated into the video, followed by a discussion of the course of the velocity. Equipment 1 ballistic unit steel sphere, d = mm scale, l = 1000 mm barrel base PHYWE velocity measurement attachment power supply unit, 5 V DC/2.4 A Figure 1: Experiment set-up P PHYWE Systeme GmbH & Co. KG All rights reserved 1

2 TEP Projectile motion with "measure Dynamics" Tasks 1. Determination of the trajectory. 2. Determination of the launching angle. 3. Determination of the initial velocity. 4. Determination of the range. 5. Determination of the maximum height. 6. Integration of the trajectory into the video. 7. Integration of the velocity vectors into the video. Set-up and procedure Set the ballistic unit up as shown in Figure 1 and adjust it by launching the steel sphere at a 90 angle, i.e. straight upwards, and by catching it in your hand. Adjust the support system so that the sphere will be launched vertically upwards. Since the launching spring of the ballistic unit has three different states of tensioning, three different initial velocities can be simulated when launching the steel sphere. Adjust a random launching angle. After the sphere has completed its trajectory, it either falls on the floor or on a table. We recommend using an empty cardboard box or similar for catching the sphere. In terms of the video that will be recorded, the following must be taken into consideration concerning the setting and positioning of the camera: Set the number of frames per second to approximately 30 fps. Select a light-coloured, homogeneous background. Provide additional lighting for the experiment. The experiment set-up should be in the centre of the video. To ensure this, position the video camera on a tripod centrally in front of the experiment set-up. The experiment set-up should fill the video image as completely as possible. The optical axis of the camera must be parallel to the experiment set-up. Position a scale in the trajectory of the sphere by way of the barrel base to ensure proper scaling. Then, the video recording process and the experiment can be started. Theory When an object with the mass m moves in a constant gravitational field (gravitational force ), the trajectory lies in a plane. If the system of coordinates is also positioned in this plane (x, y plane see Figure 2) and if the equation of motion with: is solved under the initial conditions 2 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P

3 Projectile motion with "measure Dynamics" TEP we obtain the coordinates and as a function of time t: Figure 2: Motion of a mass point under the influence of gravitational force Based on the graph that is given above, and as a function of the angle ϕ, we obtain the maximum height of the sphere from and the maximum range of the sphere from Evaluation Transfer the video that has been recorded to the computer. Then, start "measure Dynamics" and open the video under "File" "Open video...". Mark the start of the experiment ("Start selection" and "Time zero") and the end of the experiment ("End selection") in the video for further analysis via the menu line above the video. The experiment starts with the launch of the sphere and it ends after its first impact. Then, mark the distance that appears in the video under "Video analysis" "Scaling..." "Calibration" and with the aid of the scale that is included in the experiment set-up and enter the resulting distance into the input window. In addition, enter the frame rate that has been set for the recording process under "Change frame rate" and position the system of coordinates at the point where the sphere leaves the launching tube under "Origin and direction". Then, the actual motion analysis can be started under "Video analysis" "Automatic analysis" or "Manual analysis". For the automatic analysis, we recommend selecting "Motion and colour analysis" on the "Analysis" tab. Under "Options", the automatic analysis can be optimised, if necessary, e.g. by changing the sensitivity or by limiting the detection radius. Then, look for a film position in the video where the steel sphere is perfectly visible. Click the sphere. If the system recognises it, a green rectangle appears P PHYWE Systeme GmbH & Co. KG All rights reserved 3

4 TEP Projectile motion with "measure Dynamics" and the analysis can be started by clicking "Start". If the automatic analysis does not lead to any satisfying results, the series of measurements can be corrected under "Manual analysis" by manually marking the object that is to be analysed. Task 1: Determination of the trajectory. In order to display the trajectory of the sphere in graphical form, select "Display" and "Diagram", click "Options", delete all of the already existing graphs, and select the graphs x (horizontal axis) y (vertical axis). This leads to: Figure 3 shows the parabolic trajectory that could have been expected from the theory. In addition, Figure 3 provides information concerning the maximum height and range of the sphere (i.e. the distance that the sphere covers until it reaches its initial height). Details concerning the values can be found in tasks 4 and 5. Figure 3: Trajectory of the sphere Task 2: Determination of the launching angle. The launching angle of the sphere can be determined either directly via the angle scale of the launching tube or by way of the angle measurement function of "measure Dynamics". In order to use the second option, open "Measure" and then "Measure angle". Position the vertex of the angle on the lower end of the launching tube. Then, position one arm of the angle parallel to the x-axis (the colour of the ray changes to red) and the other arm of the angle along the launching tube so that the angle is located in the vertex of the angle. 4 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P

5 Projectile motion with "measure Dynamics" TEP Figure 4: Determination of the launching angle Figure 4 shows that the launching angle in this experiment is Task 3: Determination of the initial velocity In order to determine the initial velocity, extend the worksheet by clicking "New column" in the table menu line. Then, enter "v_total" (unit: "m/s"; formula: "((v_x)^2+(v_y)^2)^0.5") into the new column. While the velocity in the x-direction remains nearly constant, i.e. the velocity loss that is caused by the air drag is neglectable at the velocities that occur during this experiment, the velocity in the y-direction changes continuously due the gravitational acceleration. This means that the initial velocity can only be determined directly after the launch of the sphere. The initial velocity during this experiment is 2.50 m/s. If this method is not sufficiently precise, it is also possible to determine the velocity by way of the velocity measurement attachment. Task 4: Determination of the range. The range can be determined with the aid of Figure 3 by determining the point where the sphere has reached its initial height again. In addition, this can be verified mathematically with the aid of the values of the launching angle and initial velocity from tasks 2 and 3. The graphical method and the mathematical method provide a range of 0.55 m. This means that the theoretical equation for the range is confirmed by practical experience. Task 5: Determination of the maximum height. The maximum height can also be determined graphically with the aid of Figure 3 and also mathematically by way of the values for the launching angle and initial velocity from tasks 2 and 3 based on the theory. The height that is determined graphically is 0.22 m and the height that is determined mathematically is 0.24 m. Since the two values are very close to one another, the theoretical equation for the maximum height has been confirmed by the experiment. Task 6: Integration of the trajectory into the video. The trajectory can be integrated into the video in two different ways. One method involves the creation of a stroboscopic picture. To do so, open "Stroboscopic picture" under "Video analysis". Clicking "Start" in P PHYWE Systeme GmbH & Co. KG All rights reserved 5

6 TEP Projectile motion with "measure Dynamics" the dialogue box creates the following stroboscopic picture (it may be necessary to change the settings under "Options" in order to optimise the stroboscopic picture). The second option is to integrate the trajectory into the video. To do so, open "Filters and labels..." under "Display", click "Add new filter", and select "Symbol". Under "Filter configuration", select the tab "Limitations" and "Filter visible". Then, select "0" as the "Start selection" and "-1" as the "End selection" under "Cutting (timeline)". Select "Line" as the icon on the "Icon" tab. Select "0" under "Trace length". This means that the symbol will remain visible in the entire video. Set the "Step" to "1". On the "Data Figure 6: Stroboscopic picture of the trajectory of the sphere source" tab, select the table of the sphere under "Starting point" and "0" as the "Time increment". Select "x" as the "x-coordinate". Select "y" as the "y-coordinate". Select the table of the sphere once again under "End point" and set the "Time increment" to "+1". Once again, select "x" as the "x-coordinate" and "y" as the "y-coordinate". This leads to: Task 7: Integration of the velocity vectors into the video. In the video, the development of the velocity can be demonstrated in a particularly clear manner by integrating the velocity in the x- and y-direction as well as the total velocity. To do so, open "Filters and labels..." under "Display", click "Add new filter", and select the "Velocity arrow". Under "Filter configura- Figure 5: Integration of the trajectory into the video 6 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co. KG D Göttingen P

7 Projectile motion with "measure Dynamics" TEP tion", select the tab "Limitations" and "Filter visible". Then, select "0" as the "Start selection" and "-1" as the "End selection" under "Cutting (timeline)". On the tab "Icon", select "Arrow" as the icon, since the velocity is a vector. Select "0" under "Trace length". This means that the icon will remain visible in the entire video. Select a suitable "Step" (in this case "2") (not too few/too many vectors). On the "Data source" tab, select the table of the sphere under "Starting point" and "0" as the "Time increment". Select "x" as the "x-coordinate". Select "y" as the "y-coordinate". Select the table of the sphere once again under "End point" and set the "Time increment" to "0". In order to display the total velocity, select "v_x" as the "xcoordinate" and "v_y" as the "y-coordinate". In order to display the velocity in the x-direction, select "v_x" as the "x-coordinate" and "Fixed value" for the "y-coordinate". Set the latter to "0". In order to display the velocity in the y-direction, select "Fixed value" as the "x-coordinate" and set it to "0", and select "v_y" as the "y-coordinate". Next, choose a suitable "Stretch factor" to ensure that the vectors are neither too short nor overlapping. Then, activate "User-defined scale". The three vectors are created with identical characteristics (step, stretch factor,...). Ideally, different colours are selected for the three vectors under "Change icon" on the "Icon" tab. The arrows can be labelled under "Display" "Paint..." "Text". This leads to: Figure 7 shows the disintegration of the velocity vector into its x- and y-components. In addition, it becomes clear that the absolute value of the velocity in the x-direction remains nearly constant, which is indicated by the length of the associated vector. However, the velocity in the y-direction changes continuously. At the beginning, the absolute value decreases. At the maximum of the trajectory, it drops to zero. After the maximum, the direction of this velocity component is reversed. In addition, its absolute value increases. The changes of the velocity in the y-direction lead to a change of the resulting total velocity. Figure 7: Integration of the velocity vectors into the video P PHYWE Systeme GmbH & Co. KG All rights reserved 7

Projectile Motion Projectile motion is a special case of two-dimensional motion. A particle moving in a vertical plane with an initial velocity and experiencing a free-fall (downward) acceleration, displays

Projectile Motion! An object may move in both the x and y directions simultaneously! The form of two-dimensional motion we will deal with is called projectile motion Assumptions of Projectile Motion! The

Team: Projectile Motion So far you have focused on motion in one dimension: x(t). In this lab, you will study motion in two dimensions: x(t), y(t). This 2D motion, called projectile motion, consists of

Related topics Centripetal force, rotary motion, angular velocity, apparent force, use of an interface. Principle and task As an object moves on a circular path with a certain angular velocity, it is constantly

Mechanics Translational motions of a mass point One-dimensional motions on the linear air track LD Physics Leaflets P1.3.3.8 Uniformly accelerated motion with reversal of direction Recording and evaluating

A cannon shoots a clown directly upward with a speed of 20 m/s. What height will the clown reach? How much time will the clown spend in the air? Projectile Motion 1:Horizontally Launched Projectiles Two

Impulse and Momentum All particles with mass experience the effects of impulse and momentum. Momentum and inertia are similar concepts that describe an objects motion, however inertia describes an objects

CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal

Lab: Vectors Lab Section (circle): Day: Monday Tuesday Time: 8:00 9:30 1:10 2:40 Name Partners Pre-Lab You are required to finish this section before coming to the lab. It will be checked by one of the

Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.

2009 19 minutes Teacher Notes: Ian Walter DipAppChem; TTTC; GDipEdAdmin; MEdAdmin (part) Program Synopsis This program begins by looking at the different types of motion all around us. Forces that cause

Force and Motion Sections Covered in the Text: Chapters 4 and 8 Thus far we have studied some attributes of motion. But the cause of the motion, namely force, we have essentially ignored. It is true that

An Introduction to Using Simulink Exercises Eric Peasley, Department of Engineering Science, University of Oxford version 4.1, 2013 PART 1 Exercise 1 (Cannon Ball) This exercise is designed to introduce

Tutorial for Tracker and Supporting Software By David Chandler I use a number of free, open source programs to do video analysis. 1. Avidemux, to exerpt the video clip, read the video properties, and save

Microsoft Excel Tutorial by Dr. James E. Parks Department of Physics and Astronomy 401 Nielsen Physics Building The University of Tennessee Knoxville, Tennessee 37996-1200 Copyright August, 2000 by James

Team: Projectile Motion So far you have focused on motion in one dimension: x(t). In this lab, you will study motion in two dimensions: x(t), y(t). This 2D motion, called projectile motion, consists of

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was

1 PURPOSE ACTIVITY SIX CONSERVATION OF MOMENTUM ELASTIC COLLISIONS For this experiment, the Motion Visualizer (MV) is used to capture the motion of two frictionless carts moving along a flat, horizontal

TWO DIMENSIONAL VECTORS AND MOTION 1. Two nonzero vectors have unequal magnitudes of X and Y. Which of the following could be the length of their sum? (i) 0 (ii) X+Y (iii) X (iv) Y a. (i), (iii), and (iv)

Description Lab 5: Projectile Motion In this lab, you will examine the motion of a projectile as it free falls through the air. This will involve looking at motion under constant velocity, as well as motion

BROCK UNIVERSITY MATHEMATICS MODULES 11A.4: Maximum or Minimum Values for Quadratic Functions Author: Kristina Wamboldt WWW What it is: Maximum or minimum values for a quadratic function are the largest

In this experiment, you will be using your video equipment to evaluate two-dimensional motion. It will be necessary to plot the data in an xy-coordinate system and separate the data into x and y components.

PHYS-101 LAB-02 One- and Two-dimensional Motion 1. Objective The objectives of this experiment are: to measure the acceleration of gravity using one-dimensional motion to demonstrate the independence of

Projectile Motion Pre-lab Assignment Derive algebraic expressions for the range and total time-of-flight of a projectile launched with initial speed v o from a height h at an angle above horizontal. Hint:

55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction

Experiment 2: Conservation of Momentum Learning Goals After you finish this lab, you will be able to: 1. Use Logger Pro to analyze video and calculate position, velocity, and acceleration. 2. Use the equations

Physics 161 FREE FALL Introduction This experiment is designed to study the motion of an object that is accelerated by the force of gravity. It also serves as an introduction to the data analysis capabilities

Motion in Two Dimensions 1. The position vector at t i is r i and the position vector at t f is r f. The average velocity of the particle during the time interval is a.!!! ri + rf v = 2 b.!!! ri rf v =

VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how

2 BUNGEE JUMP ACCELERATIONS LAB MECH 25.COMP From Physics with Computers, Vernier Software and Technology, 2003 INTRODUCTION In this experiment, you will investigate the accelerations that occur during

Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

Projectile Motion - Worksheet From the given picture; you can see a skateboarder jumping off his board when he encounters a rod. He manages to land on his board after he passes over the rod. 1. What is

1. The acceleration due to gravity on the surface of planet X is 19.6 m/s 2. If an object on the surface of this planet weighs 980. newtons, the mass of the object is 50.0 kg 490. N 100. kg 908 N 2. If

Chapter 3: Falling Objects and Projectile Motion 1. Neglecting friction, if a Cadillac and Volkswagen start rolling down a hill together, the heavier Cadillac will get to the bottom A. before the Volkswagen.

Open GeoGebra & Format Worksheet 1. Close the Algebra view tab by clicking on the in the top right corner. 2. Show the grid by clicking on the show grid icon, located under the toolbar. 3. Select the Move

FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

Quickstart for Web and Tablet App What is GeoGebra? Dynamic Mathematic Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,

MASSACHUSETTS INSTITUTE OF TECHNOLOY Department of Physics 8. Spring 5 OBJECTIVES Experiment 7: Forces and Torques on Magnetic Dipoles 1. To measure the magnetic fields due to a pair of current-carrying

ORBITAL MECHANICS 1 PURPOSE The purpose of this laboratory project is to calculate, verify and then simulate various satellite orbit scenarios for an artificial satellite orbiting the earth. First, there

Chapter 2 One Dimensional Kinematics How would you describe the following motion? Ex: random 1-D path speeding up and slowing down In order to describe motion you need to describe the following properties.

Quickstart for Desktop Version What is GeoGebra? Dynamic Mathematics Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,

Name: Class: Date: Magnetism 22.1 Conceptual Questions 1) A proton, moving north, enters a magnetic field. Because of this field, the proton curves downward. We may conclude that the magnetic field must

Free Fall and Projectile motion 1. Introduction Free fall is the motion of a fallin body under the effect of the ravitational field only. Projectile motion is the motion of a body thrown with an initial

Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time

2 Bungee Jump Accelerations Experiment 7 In this experiment, you will investigate the accelerations that occur during a bungee jump. The graph below records the acceleration vs. time for an actual bungee

Worksheet #1 Free Body or Force diagrams Drawing Free-Body Diagrams Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation.

Acceleration of Gravity Introduction: In this experiment, several objects' motion are studied by making several measurements of the objects position (or displacement) at different times. Since the objects

Reavis High School Physics Honors Curriculum Snapshot Unit 1: Mathematical Toolkit Students will be able to: state definition for physics; measure length using a meter stick; measure the time with a stopwatch

Physics 1 Vectors Cartesian Coordinate System Also called rectangular coordinate system x- and y- axes intersect at the origin Points are labeled (x,y) Polar Coordinate System Origin and reference line

Bungee Jump Accelerations Computer 7 In this experiment, you will investigate the accelerations that occur during a bungee jump. The graph below records the acceleration vs. time for an actual bungee jump,

Projectile Motion Introduction: A projectile is a body in free fall that is subject only to the forces of gravity (9.81ms ²) and air resistance. An object must be dropped from a height, thrown vertically

APPENDIX A STSE Science-Technology-Society and the Environment PHYSICS 304 CURRICULUM GUIDE 115 Important Note These STSE modules are intended for teacher reference. Each is designed to target specific

Newton s Second Law Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart will be developed

Uniformly Accelerated Motion Under special circumstances, we can use a series of three equations to describe or predict movement V f = V i + at d = V i t + 1/2at 2 V f2 = V i2 + 2ad Most often, these equations

CHAPTER 3: GRAPHS OF QUADRATIC RELATIONS Specific Expectations Addressed in the Chapter Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology

L06-1 Name Date Partners LAB 6 - GRAVITATIONAL AND PASSIVE FORCES OBJECTIVES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies

Motion in one and two dimensions: Lesson 1 Semi-notes Motion Lesson 1: Review of Basic Motion Note. For these semi notes we will use the bold italics convention to represent vectors. Complete the following

Motion and Forces in Two Dimensions Sec. 7.1 Forces in Two Dimensions 1. A Review of Vector Addition. Forces on an Inclined Plane 3. How to find an Equilibrant Vector 4. Projectile Motion Objectives Determine